Abstract

The formulation of unobserved components models raises some relevant interpretative issues, owing to the existence of alternative observationally equivalent specifications, differing for the timing of the disturbances and their covariance matrix. We illustrate them with reference to unobserved components models with ARMA(m, m) reduced form, performing the decomposition of the series into an ARMA(m, q) signal, $q\le m,$ and a noise component. We provide a characterization of the set of covariance structures that are observationally equivalent, when the models are formulated both in the future and the contemporaneous forms. Hence, we show that, while the point predictions and the contemporaneous real time estimates are invariant to the specification of the disturbances covariance matrix, the reliability cannot be identified, except for special cases requiring $q<m-1.$

摘要

由于存在替代的观测等效规格，扰动时间及其协方差矩阵不同，因此未观测分量模型的表述引起了一些相关的解释性问题。我们参考具有ARMA（m，m）简化形式的未观察到的组件模型对它们进行说明，将序列分解为ARMA（m，q）信号，$q\le 米，$和噪声成分。当模型在将来和同时期形式下都形成时，我们提供了一组在观察上等效的协方差结构的特征。因此，我们表明，尽管点预测和实时实时估计对于扰动协方差矩阵的规范是不变的，但除非需要特殊情况，否则无法确定可靠性。$q<米-\mathrm{1个}。$